What you still might want to know about microarrays. Brixen 2011 Wolfgang Huber EMBL

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1 What you still might want to know about microarrays Brixen 2011 Wolfgang Huber EMBL

2 Brief history Late 1980s: Lennon, Lehrach: cdnas spotted on nylon membranes 1990s: Affymetrix adapts microchip production technology for in situ oligonucleotide synthesis (commercial, patent-fenced) 1990s: Brown lab in Stanford develops two-colour spotted array technology (open and free) 1998: Yeast cell cycle expression profiling on spotted arrays (Spellmann) and Affymetrix (Cho) 1999: Tumor type discrimination based on mrna profiles (Golub) 2000-ca. 2004: Affymetrix dominates the microarray market Since ~2003: Nimblegen, Illumina, Agilent (and many others) Throughout 2000 s: CGH, CNVs, SNPs, ChIP, tiling arrays Since ~2007: Next-generation sequencing (454, Solexa, ABI Solid,...)

3 Oligonucleotide microarrays

4 Base Pairing Ability to use hybridisation for constructing specific + sensitive probes at will is unique to DNA (cf. proteins, RNA, metabolites)

5 Oligonucleotide microarrays Hybridized Probe Cell GeneChip * Target - single stranded cdna oligonucleotide probe 1.28cm Image of array after hybridisation and staining * * * * 5µm millions of copies of a specific oligonucleotide probe molecule per cell up to 6.5 Mio different probe cells

6 Probe sets

7 Terminology for transcription arrays Each target molecule (transcript) is represented by several oligonucleotides of (intended) length 25 bases Probe: one of these 25-mer oligonucleotides Probe set: a collection of probes (e.g. 11) targeting the same transcript MGED/MIAME: probe is ambiguous! Reporter: the sequence Feature: a physical patch on the array with molecules intended to have the same reporter sequence (one reporter can be represented by multiple features)

8 Image analysis several dozen pixels per feature segmentation summarisation into one number representing the intensity level for this feature CEL file

9 µarray data arrays: probes = gene-specific DNA strands

10 µarray data samples: mrna from tissue biopsies, cell lines arrays: probes = gene-specific DNA strands

11 µarray data samples: mrna from tissue biopsies, cell lines arrays: probes = gene-specific DNA strands

12 µarray data samples: mrna from tissue biopsies, cell lines fluorescent detection of the amount of sample-probe binding arrays: probes = gene-specific DNA strands tissue A tissue B tissue C ErbB VIM ALDH CASP LAMA MCAM

13 Microarray Infrastructure in Bioconductor

14 Platform-specific data import and initial processing Affymetrix 3 IVT (e.g. Human U133 Plus 2.0, Mouse ): affy Affymetrix Exon (e.g. Human Exon 1.0 ST): oligo, exonmap, xps Affymetrix SNP arrays: oligo Nimblegen tiling arrays (e.g. for ChIP-chip): Ringo Affymetrix tiling arrays (e.g. for ChIP-chip): Starr Illumina bead arrays: beadarray, lumi

15 Flexible data import Using generic R I/O functions and constructors Biobase limma Chapter Two Color Arrays in the user-book. limma user guide

16 Normalisation and quality assessment preprocesscore limma vsn arrayqualitymetrics

17 featuredata ( AnnotatedDataframe ) Sequence Target gene ID NChannelSet assaydata can contain N=1, 2,..., matrices of the same size Physical Physical coordinates D coordinates Sequence Target gene ID labeldescription varmetadata Sample-ID red Sample-ID red Sample-ID green Sample-ID blue Array-ID Sample-ID green Array ID Sample-ID blue phenodata ( AnnotatedDataframe ) labeldescription R G B channeldescription _ALL_

18 Annotation / Metadata Keeping data together with the metadata (about reporters, target genes, samples, experimental conditions,...) is one of the major principles of Bioconductor avoid alignment bugs facilitate discovery Often, the same microarray design is used for multiple experiments. Duplicating that metadata every time would be inefficient, and risk versioning mismatches instead of featuredata, just keep a pointer to an annotation package. (In principle, one could also want to do this for samples.)

19 For affy: Annotation infrastructure for Affymetrix hgu133plus2.db all available information about target genes hgu133plus2cdf maps the physical features on the array to probesets hgu133plus2probe nucleotide sequence of the features (e.g. for gcrma)

20 Genotyping crlmm Genotype Calling (CRLMM) and Copy Number Analysis tool for Affymetrix SNP 5.0 and 6.0 and Illumina arrays. snpmatrix... others See also: Genome-wide association study of CNVs in 16,000 cases of eight common diseases and 3,000 shared controls, The Wellcome Trust Case Control Consortium, Nature 464, (Box 1).

21 Gene expression analysis with microarrays

22 Microarray Analysis Tasks Data import reformating and setup/curation of the metadata Normalisation Quality assessment & control Differential expression Using gene-level annotation Gene set enrichment analysis Clustering & Classification Integration of other datasets

23 What is wrong with microarray data? Many data are measured in definite units: time in seconds lengths in meters energy in Joule, etc. Climb Mount Plose (2465 m) from Brixen (559 m) with weight of 76 kg, working against a gravitation field of strength 9.81 m/s 2 : ( ) m kg m/s 2 = kg m 2 s -2 = kj

24 What is wrong with microarray data? Many data are measured in definite units: time in seconds lengths in meters energy in Joule, etc. Climb Mount Plose (2465 m) from Brixen (559 m) with weight of 76 kg, working against a gravitation field of strength 9.81 m/s 2 : ( ) m kg m/s 2 = kg m 2 s -2 = kj

25 A complex measurement process lies between mrna concentrations and intensities o RNA degradation o amplification efficiency o reverse transcription efficiency o hybridization efficiency and specificity o labeling efficiency o quality of actual probe sequences (vs intended) o scratches and spatial gradients on the array o cross-talk across features o crosshybridisation o optical noise o image segmentation o signal quantification o signal "preprocessing"

26 A complex measurement process lies between mrna concentrations and intensities o RNA degradation o amplification efficiency o reverse transcription efficiency o hybridization efficiency and specificity o labeling efficiency o quality of actual probe sequences (vs intended) o scratches and spatial gradients on the array o crosshybridisation o optical noise o image segmentation o signal quantification The problem is less that these steps are o not cross-talk perfect ; it is that they vary across from features array to array, experiment to experiment. o signal "preprocessing"

27 Background signal and non-linearities

28 mild non-linearity spike-in data log 2 Cope et al. Bioinformatics 2003

29 ratio compression nominal 3:1 nominal 1:1 nominal 1:3 Yue et al., (Incyte Genomics) NAR (2001) 29 e41

30 Preprocessing Terminology Calibration, normalisation: adjust for systematic drifts associated with dye, array (and sometimes position within array) Background correction: adjust for the non-linearity at the lower end of the dynamic range Transformation: bring data to a scale appropriate for the analysis (e.g. logarithm; variance stabilisation) Log-ratio: adjust for unknown scale (units) of the data Existing approaches differ in the order in which these steps are done, some are exactly stepwise ( greedy ), others aim to gain strength by doing things simultaneously.

31 Statistical issues

32 Which genes are differentially transcribed? same-same log-ratio

33 Which genes are differentially transcribed? same-same tumor-normal log-ratio

34 Sources of variation amount of RNA in the biopsy efficiencies of -RNA extraction -reverse transcription -labeling -fluorescent detection probe purity and length distribution spotting efficiency, spot size cross-/unspecific hybridization stray signal

35 Sources of variation amount of RNA in the biopsy efficiencies of -RNA extraction -reverse transcription -labeling -fluorescent detection probe purity and length distribution spotting efficiency, spot size cross-/unspecific hybridization stray signal Systematic o similar effect on many measurements o corrections can be estimated from data

36 Sources of variation amount of RNA in the biopsy efficiencies of -RNA extraction -reverse transcription -labeling -fluorescent detection probe purity and length distribution spotting efficiency, spot size cross-/unspecific hybridization stray signal Systematic o similar effect on many measurements o corrections can be estimated from data Calibration

37 Sources of variation amount of RNA in the biopsy efficiencies of -RNA extraction -reverse transcription -labeling -fluorescent detection Systematic o similar effect on many measurements o corrections can be estimated from data probe purity and length distribution spotting efficiency, spot size cross-/unspecific hybridization stray signal Stochastic o too random to be explicitely accounted for o remain as noise Calibration

38 Sources of variation amount of RNA in the biopsy efficiencies of -RNA extraction -reverse transcription -labeling -fluorescent detection Systematic o similar effect on many measurements o corrections can be estimated from data probe purity and length distribution spotting efficiency, spot size cross-/unspecific hybridization stray signal Stochastic o too random to be explicitely accounted for o remain as noise Calibration Error model

39 Why do you need normalisation (a.k.a. calibration)?

40 Systematic drift effects From: lymphoma dataset vsn package Alizadeh et al., Nature 2000

41 Quantile normalisation Within each column (array), replace the intensity values by their rank For each rank, compute the average of the intensities with that rank, across columns (arrays) Replace the ranks by those averages features (genes) arrays (samples) Ben Bolstad 2001

42

43 Quantile normalisation

44 Quantile normalisation + Simple, fast, easy to implement

45 Quantile normalisation + Simple, fast, easy to implement + Always works, needs no user interaction / tuning

46 Quantile normalisation + Simple, fast, easy to implement + Always works, needs no user interaction / tuning + Non-parametric: can correct for quite nasty non-linearities (saturation, background) in the data

47 Quantile normalisation + Simple, fast, easy to implement + Always works, needs no user interaction / tuning + Non-parametric: can correct for quite nasty non-linearities (saturation, background) in the data - Always "works", even if data are bad / inappropriate

48 Quantile normalisation + Simple, fast, easy to implement + Always works, needs no user interaction / tuning + Non-parametric: can correct for quite nasty non-linearities (saturation, background) in the data - Always "works", even if data are bad / inappropriate - May be conservative: rank transformation looses information - may yield less power to detect differentially expressed genes

49 Quantile normalisation + Simple, fast, easy to implement + Always works, needs no user interaction / tuning + Non-parametric: can correct for quite nasty non-linearities (saturation, background) in the data - Always "works", even if data are bad / inappropriate - May be conservative: rank transformation looses information - may yield less power to detect differentially expressed genes - Aggressive: if there is an excess of up- (or down) regulated genes, it removes not just technical, but also biological variation

50 Estimating relative expression (fold-changes)

51 ratios and fold changes Fold changes are useful to describe continuous changes in expression x3 x1.5 A B C But what if the gene is off (below detection limit) in one condition? ?? A B C

52 ratios and fold changes The idea of the log-ratio (base 2) 0: no change +1: up by factor of 2 1 = 2 +2: up by factor of 2 2 = 4-1: down by factor of 2-1 = 1/2-2: down by factor of 2-2 = ¼

53 ratios and fold changes The idea of the log-ratio (base 2) 0: no change +1: up by factor of 2 1 = 2 +2: up by factor of 2 2 = 4-1: down by factor of 2-1 = 1/2-2: down by factor of 2-2 = ¼ A unit for measuring changes in expression: assumes that a change from 1000 to 2000 units has a similar biological meaning to one from 5000 to data reduction

54 ratios and fold changes The idea of the log-ratio (base 2) 0: no change +1: up by factor of 2 1 = 2 +2: up by factor of 2 2 = 4-1: down by factor of 2-1 = 1/2-2: down by factor of 2-2 = ¼ A unit for measuring changes in expression: assumes that a change from 1000 to 2000 units has a similar biological meaning to one from 5000 to data reduction What about a change from 0 to 500? - conceptually - noise, measurement precision

55 Two component error model and variance stabilisation

56 The two-component model raw scale log scale B. Durbin, D. Rocke, JCB 2001

57 The two-component model multiplicative noise additive noise raw scale log scale B. Durbin, D. Rocke, JCB 2001

58 The two-component model multiplicative noise additive noise We will see something similar in with short read count data - just replace the additive component with Poisson raw scale log scale B. Durbin, D. Rocke, JCB 2001

59 The additive-multiplicative error model variance var = mean 2 additive component sqrt(variance) multiplicative component mean mean

60 The additive-multiplicative error Trey Ideker et al.: JCB (2000) model David Rocke and Blythe Durbin: JCB (2001), Bioinformatics (2002) Use for robust affine regression normalisation: W. Huber, Anja von Heydebreck et al. Bioinformatics (2002). For background correction in RMA: R. Irizarry et al., Biostatistics (2003).

61 The two component model measured intensity = offset + gain true abundance a i per-sample offset ε ik additive noise b i per-sample gain factor b k sequence-wise probe efficiency η ik multiplicative noise

62 variance stabilizing transformations X u a family of random variables with E(X u ) = u and Var(X u ) = v(u). Define Then, var f(x u ) does not depend on u Derivation: linear approximation, relies on smoothness of v(u).

63 variance stabilizing transformation f(x) x

64 variance stabilizing transformations 1.) constant variance ( additive ) 2.) constant CV ( multiplicative ) 3.) offset 4.) additive and multiplicative

65 the glog transformation P. Munson, 2001 D. Rocke & B. Durbin, ISMB 2002 W. Huber et al., ISMB 2002

66 glog raw scale log glog difference log-ratio generalized log-ratio

67 glog raw scale log glog difference log-ratio generalized log-ratio variance: constant part proportional part

68 Parameter estimation

69 Parameter estimation

70 Parameter estimation

71 Parameter estimation o maximum likelihood estimator: straightforward but sensitive to deviations from normality

72 Parameter estimation o maximum likelihood estimator: straightforward but sensitive to deviations from normality o model holds for genes that are unchanged; differentially transcribed genes act as outliers.

73 Parameter estimation o maximum likelihood estimator: straightforward but sensitive to deviations from normality o model holds for genes that are unchanged; differentially transcribed genes act as outliers. o robust variant of ML estimator, à la Least Trimmed Sum of Squares regression.

74 Parameter estimation o maximum likelihood estimator: straightforward but sensitive to deviations from normality o model holds for genes that are unchanged; differentially transcribed genes act as outliers. o robust variant of ML estimator, à la Least Trimmed Sum of Squares regression. o works well as long as <50% of genes are differentially transcribed (and may still work otherwise)

75 usual log-ratio 'glog' (generalized log-ratio) c 1, c 2 are experiment specific parameters (~level of background noise)

76 Variance-bias trade-off and shrinkage estimators Shrinkage estimators: a general technology in statistics: pay a small price in bias for a large decrease of variance, so overall the mean-squared-error (MSE) is reduced. Particularly useful if you have few replicates. Generalized log-ratio is a shrinkage estimator for log fold change

77 other background correction methods

78 Background correction 0 pm 750 fm 500 fm 1 pm Irizarry et al. Biostatistics 2003

79 RMA Background correction Irizarry et al. (2002)

80 Background correction: raw intensities x biased background correction s=e[s data] log 2 (s) unbiased background correction s=x-b glog 2 (s data)?

81 Comparison between RMA and VSN background correction vsn package vignette

82 Summaries for Affymetrix genechip probe sets

83 Data and notation PM ikg, MM ikg = Intensities for perfect match and mismatch probe k for gene g on chip i i = 1,, n k = 1,, J one to hundreds of chips usually 11 probe pairs g = 1,, G tens of thousands of probe sets. Tasks: calibrate (normalize) the measurements from different chips (samples) summarize for each probe set the probe level data, i.e., 11 PM and MM pairs, into a single expression measure. compare between chips (samples) for detecting differential expression.

84 Expression measures: MAS 4.0 Affymetrix GeneChip MAS 4.0 software used AvDiff, a trimmed mean: o sort d k = PM k -MM k o exclude highest and lowest value o K := those pairs within 3 standard deviations of the average

85 Expression measures MAS 5.0 Instead of MM, use "repaired" version CT CT = MM if MM<PM = PM / "typical log-ratio" if MM>=PM Signal = Weighted mean of the values log(pm-ct) weights follow Tukey Biweight function (location = data median, scale a fixed multiple of MAD)

86 Expression measures: Li & Wong dchip fits a model for each gene where φ i : expression measure for the gene in sample i θ k : probe effect φ i is estimated by maximum likelihood

87

88 Expression measures RMA: Irizarry et al. (2002) dchip RMA b i is estimated using the robust method median polish (successively remove row and column medians, accumulate terms, until convergence).

89 Quality assessment

90 Quality assessment arrayqualitymetrics example quality report

91 References Bioinformatics and computational biology solutions using R and Bioconductor, R. Gentleman, V. Carey, W. Huber, R. Irizarry, S. Dudoit, Springer (2005). Variance stabilization applied to microarray data calibration and to the quantification of differential expression. W. Huber, A. von Heydebreck, H. Sültmann, A. Poustka, M. Vingron. Bioinformatics 18 suppl. 1 (2002), S96-S104. Exploration, Normalization, and Summaries of High Density Oligonucleotide Array Probe Level Data. R. Irizarry, B. Hobbs, F. Collins,, T. Speed. Biostatistics 4 (2003) Error models for microarray intensities. W. Huber, A. von Heydebreck, and M. Vingron. Encyclopedia of Genomics, Proteomics and Bioinformatics. John Wiley & sons (2005). Normalization and analysis of DNA microarray data by self-consistency and local regression. T.B. Kepler, L. Crosby, K. Morgan. Genome Biology. 3(7):research0037 (2002) Statistical methods for identifying differentially expressed genes in replicated cdna microarray experiments. S. Dudoit, Y.H. Yang, M. J. Callow, T. P. Speed. Technical report # 578, August 2000 (UC Berkeley Dep. Statistics) A Benchmark for Affymetrix GeneChip Expression Measures. L.M. Cope, R.A. Irizarry, H. A. Jaffee, Z. Wu, T.P. Speed. Bioinformatics (2003)....many, many more...

92 Acknowledgements Anja von Heydebreck (Merck, Darmstadt) Robert Gentleman (Genentech, San Francisco) Günther Sawitzki (Uni Heidelberg) Martin Vingron (MPI, Berlin) Rafael Irizarry (JHU, Baltimore) Terry Speed (UC Berkeley) Jörn Tödling (Inst. Curie, Paris) Lars Steinmetz (EMBL Heidelberg) Audrey Kauffmann (Novartis, Basel)

93

94 What about non-linear effects o Microarrays can be operated in a linear regime, where fluorescence intensity increases proportionally to target abundance (see e.g. Affymetrix dilution series) Two reasons for non-linearity: o At the high intensity end: saturation/quenching. This can (and should) be avoided experimentally - loss of data! o At the low intensity end: background offsets, instead of y=k x we have y=k x+x 0, and in the log-log plot this can look curvilinear. But this is an affine-linear effect and can be correct by affine normalization. Local polynomial regression may be OK, but tends to be less efficient.

95 Non-linear or affine linear?